Need Technique for Projecting Countries onto the Earth
You could:

Select all you countries and join them with CtrlJ
Create 2 grids (delete faces only, keep the edges), one for the front, the other for the side view:



Select one grid, shift select the pink object, go in Front view, go in Edit mode and in the header menu, choose Mesh &gt; Knife Project. In the Operator box, enable the Cut Through option. Do the same for the second grid (side view), here is what it gives:



You could as well use a sphere as a grid:



Give your pink object a Shrinkwrap modifier, increase slightly the Offset so that the sphere and the pink object don't cross each other:


You can give it a bit of thickness with the Solidify modifier.